提出新分解方法提升有界数据降维稳定性，适合癌症甲基化分析。
Doubly Non-Central Beta Matrix Factorization for Stable Dimensionality Reduction of Bounded Support Matrix Data
- 基于双非中心贝塔矩阵分解，无因子列数限制。
- 在预测与计算效率上相当，但超稳定抗超参扰动。
- 适用于需高可信因子的生物医学假说验证场景。
针对具有有界取值的大型数据矩阵（如大规模DNA甲基化研究），本文提出一种可解释且计算高效的矩阵分解方法。该方法采用无需约束因子列数的Tucker表示，并推导出高效采样算法求解。通过可预测性、可计算性和稳定性三方面评估，实证表明：本方法在留出预测和计算复杂度上与当前先进方法相当，但在超参数变化下的稳定性显著更优。更高的稳定性使结果在生成和检验科学假设（如癌症样本甲基化分析）时更具可信度。
原文摘要 · Abstract (English)
We consider the problem of developing interpretable and computationally efficient matrix decomposition methods for matrices whose entries have bounded support. Such matrices are found in large-scale DNA methylation studies and many other settings. Our approach decomposes the data matrix into a Tucker representation wherein the number of columns in the constituent factor matrices is not constrained. We derive a computationally efficient sampling algorithm to solve for the Tucker decomposition. We evaluate the performance of our method using three criteria: predictability, computability, and stability. Empirical results show that our method has similar performance as other state-of-the-art approaches in terms of held-out prediction and computational complexity, but has significantly better performance in terms of stability to changes in hyper-parameters. The improved stability results in higher confidence in the results in applications where the constituent factors are used to generate and test scientific hypotheses such as DNA methylation analysis of cancer samples.
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